The average amount of money spent for lunch per person in the college cafeteria is $6.89 and the standard deviation is $2.47. Suppose that 9 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N b. What is the distribution of ? - N 66666 c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $7.8151 and $8.2368. d. For the group of 9 patrons, find the probability that the average lunch cost is between $7.8151 and $8.2368. e. For part d), is the assumption that the distribution is normal necessary? O Yes No